I will present examples of an action of a totally disconnected group G on a factor Q such that intermediate subfactors between Q and the crossed-product correspond to closed subgroups of G. This extends previous work of Choda and Izumi-Longo-Popa. I will discuss about the analytical difference with the case of actions of discrete groups regarding the existence of conditional expectations or operator valued weights. Finally I will talk about intermediate subfactors in the context of actions of Hecke pairs of groups. This is a joint work with Rémi Boutonnet.

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